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Measures of weak noncompactness and fixed point theory in Banach algebras satisfying condition (<i>P</i>) [PDF]

Fixed Point Theory, 2017
Afif Ben Amar, Donal O’Regan
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ON THE VOLTERRA-STIELTJES INTEGRAL EQUATION AND AXIOMATIC MEASURES OF WEAK NONCOMPACTNESS [PDF]

International Journal of Apllied Mathematics, 2019
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Essential spectra of some matrix operators by means of measures of weak noncompactness [PDF]

Operators and Matrices, 2014
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On measures of weak noncompactness [PDF]

Annali Di Matematica Pura Ed Applicata, 1988
The authors give an axiomatic definition of measures of weak noncompactness which is in some sense parallel to \textit{B. N. Sadovskij}'s definition of measures of (strong) noncompactness [see e.g. Usp. Mat. Nauk 27, No.1, 81-146 (1972; Zbl 0243.47033)]. The first explicit measure of weak noncompactness is due to \textit{F. S. de Blasi} [Bull.
Józef Banas
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Measure of super weak noncompactness in some Banach sequence spaces

Journal of Mathematical Analysis and Applications, 2021
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Kun Tu
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A Measure of Weak Noncompactness in $$L^1({\mathbb {R}}^N)$$ and Applications

Mediterranean Journal of Mathematics, 2022
A new measure of weak noncompactness in the Banach space \(L^1(\mathbb{R}^N)\) is proposed. It is a generalization of the Banas-Knap measure of weak noncompactness, which in turn is a generalization of the De Blasi measure of weak noncompactness. Then, the multidimensional nonlinear functional integral equation \[ u(t,x)=f(t,x,u(t,x))+ g\left( t,x ...
S Djebali
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Existence of fixed points and measures of weak noncompactness

Nonlinear Analysis: Theory, Methods & Applications, 2009
The author proves the existence of fixed points of an operator \(A\) which is defined on a closed convex subset \(M\) of a Banach space \(X\) into itself and satisfies the following properties: (a) the measure of weak noncompactness of \(A(C)\) where \(C\subset M\) is not relatively weakly compact is strictly less than the measure of weak compactness ...
Jesus Garcia-Falset
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Weakly demicompact linear operators and axiomatic measures of weak noncompactness

Mathematica Slovaca, 2019
Abstract In this paper, we study the relationship between the class of weakly demicompact linear operators, introduced in [KRICHEN, B.—O’REGAN, D.: On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), 625–630], and measures of weak noncompactness of linear operators with respect to an axiomatic one. Moreover,
Bilel Krichen, Donal O'Regan
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Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the lebesgue space

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author shows that, for a subset \(X\) of \(L_1\) which is compact in measure, the continuity, demicontinuity, and weak sequential continuity of \(T: X\to X\) are equivalent. This makes it possible to enlarge the applicability of fixed point theorems involving weakly condensing operators.
Józef Banas
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Measure of weak noncompactness, some new properties in Fredholm theory, characterization of the Schechter essential spectrum and application to transport operators

Ricerche Di Matematica, 2012
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Aref Jeribi, Maher Mnif
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